The judge heard Guzmán's legal team's appeals against the extradition decision on September 26, and it's not yet known when that judge will return a decision. Once he does, however, whichever side the ruling goes against is likely to appeal, likely extending the process for weeks more.

For its part, Guzmán's legal team disputed Sales' timeline. José Refugio Rodríguez, one of Guzmán's attorneys, said in an interview that the extradition petitions didn't all meet the conditions under which the transfer could be carried out by the date mentioned by Sales, according to Mexican newspaper Excelsior.

Sales "can calculate, he can have a personal opinion. I see it very difficult (to be) from here to January," Rodríguez said in the interview, according to La Prensa.

The extradition process against Guzmán has proceeded slowly since his recapture in January this year, when Mexican President Enrique Peña Nieto said his government planned to send the kingpin north.

Experts have estimated that could take several years — possibly up to six — for Guzmán to be extradited to a US court, and other major kingpins captured in Mexico have sweated out multiyear extradition battles before eventually landing in the US.

The Mexican government also has a way to circumvent the legal battle around Guzmán, acting independent of the judiciary in order to carry out the extradition.

"As a technical matter, the Mexican executive [branch] is not at all dependent on the Mexican judicial system to approve of extradition," Peter Vincent, a former legal adviser at the US Department of Homeland Security, told Business Insider earlier this year. "It in fact has unilateral authority ... to ultimately approve of extradition, because extradition is after all a diplomatic matter, best handled by the executive branch."

The Mexican government has exercised this authority in the past, sending cartel chief Benjamin Arellano Felix, a one-time rival of Guzmán, to the US in 2008 after deciding that he would not face double jeopardy in a US court.

Comments from Rodríguez, Guzmán's attorney, suggest he is aware of this possibility.

"If the subject of the extradition is not politicized," he said, "we have means to avoid it."